Thursday, March 08, 2007

Pure Evil

A conversation I had with a graduate student, maybe ten years ago.

Student: I hear Bill Gates wants "P ≠ NP" proven at Microsoft and is hiring smart mathematicians to do so.
Me: All the power to him.
Student: How can you say that? Isn't Bill Gates pure evil.

There is a tendency among many academics to think of the world in black and white and in particular consider some people or institutions truly evil. Elsevier, George Bush (and Republicans in general) and the RIAA only desire to destroy everything good about academic publishing, the US, and personal freedom respectively. Bill Gates certainly used to be in that category but has softened now that Microsoft has lost some dominance and hires many of our friends.

Scientist tend to believe the world works by simple rules and we reinforce these viewpoints by only hanging out with other scientists like ourselves. The Internet has only made things worse, as we tend to only read stuff written by people who already agree with us.

I certainly don't defend all the policies of Elsevier, George, and the recording industry, but they don't have agendas of evil and in fact often have the same long-term goals that many of us share. We don't always share the same strategies but it would be better to work with them then to shut them out entirely by having no faith that they can do any good.

41 comments:

  1. You write:
    I certainly don't defend all the policies of Elsevier, George, and the recording industry, but they don't have agendas of evil and in fact often have the same long-term goals that many of us share.

    Actually, they don't. Their goal is to make a lot of money. For most of "us", the goal is to publish many STOC/FOCS papers.

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  2. I thought that george's
    long term goal is to spread his religion. It may be
    a good thing, and it
    is definitely not evil,
    but i doubt
    that it is shared by
    many of us here.

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  3. anonymous1 wrote: Actually, they don't. Their goal is to make a lot of money. For most of "us", the goal is to publish many STOC/FOCS papers.

    the long-term goal of publishing multiple papers is to get a job that pays. those who are doing it for scientific principles must certainly question why 90% of all papers out there are insignificant.

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  4. lance wrote:
    The Internet has only made things worse, as we tend to only read stuff written by people who already agree with us.

    very astute observation. how many of us have stopped reading newspapers online with biases that are different from ours?

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  5. why 90% of all papers out there are insignificant.

    Ah, the age old canard, which of course it doesn't include your papers which are all top notch. The point is science is built incrementally and one never knows where the next insight will come from that solves a major problem. Andrew Wiles was reading an "insignificant" paper containing some rather boring calculation which happened to be the missing key in his original proof. Later on an error in his proof was found elsewhere which he had failed to resolve. Eventually he decided, just for the sake of completeness, to fully characterize why his proof wasn't working. Talk about a seemingly insignificant paper: "why my proof is wrong and unfixable" by Andrew Wiles. Lo and behold, turned out that the cases in which his proof didn't work were already taken care of with another "insignificant" failed result he had attempted earlier.

    So in the end at least three "insignificant" papers were instrumental in his proof. That is why the field readily publishes so much "middle-of-the-road" papers. A few of those papers end up providing tools and insights to attack really big problems.

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  6. ...but they don't have agendas of evil...

    You have to define evil very narrowly in order to excuse the second item in your list.

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  7. Just a minor comment, that Bill Gates is not pure evil. His charitable foundation is very generous and helps a lot of people... Microsoft, now THAT'S pure evil...

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  8. Ars Mathematica has a link to a George Dantzig memorial article that provides abundant evidence as to the retrospective importance of mathematical work that was regarded as uninspiring at first.

    Note: ref [1] of the above, "An Interview with George Dantzig", is also worth reading, but AFAICT is not available on-line.

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  9. It's difficult to find people with soft hearts who are capable of hard thinking. Actually, it's difficult to try to be such a person.

    But has the internet really made things worse? I use Google News and some other sources to read papers I never would have otherwise, and I use the internet to actively seek out opinions different from my own.

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  10. Annonymous TCS researcher3:34 PM, March 08, 2007

    I agree with anonymous 5. The mindset that only great results should be published will not lead to more great results, but fewer. Not only because valuable insights will be lost, but also because that would lead to too much pressure on researchers. How can one even start working if one believes that the end result must always be a great theorem?

    I have a personal story that illustates both points. A few years ago, I had a collaboration with a mathematian and I offered him to start work on a new project. He informed me that his colleagues would not consider this project worthwhile because it could lead only to a "minor result", and that mathematicians have very high standards. He probably shared this opinion, but I don't remember that he said that explicitly. In any case, I ended up working on this project on my own, and published the "minor result".
    It turned out that the resulting paper contained key insights for a further result which, while perhaps not of FLT caliber, I consider one of my best.
    Meanwhile the mathematician, who had not published a lot recently, began to show up less and less frequntly at the lab, and then he quit math research entirely.

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  11. this is anon3. i entirely support anon5 and anon10 in their claims that small results should be written up and research is done only incrementally.

    however i have severe reservations about:
    1. publishing them merely for the sake of adding to one's publications.
    2. publishing them without some context of how they even might be useful in the context of larger problems.
    3. publishing them without regard for how unfamiliar researchers might go about separating the grain from the chaff.

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  12. I agree with the general principle of the original post. But even though Elsevier (just to focus on one of Lance's example) isn't "evil" and there are many non-zero-sum compromises we can make with them, the long-term calculus might be different.

    For example, in the short-term they might add to the diversity of journals out there, but if the community manages to take a hard-line on them then in the long-term we might have the same or greater diversity of journals but with fewer rents being paid to parasitic corporations that spend them organizing arms fairs.

    Of course the goal isn't to crush Elsevier, but to exert pressure on them to change. "Shut[ting] them out entirely" is a straw man.

    A good analogy is S. Africa under apartheid. Of course the boycott was meant to encourage reform and not permanent isolation; at the same time, it would have been inappropriate to "work with them" on the "long-term goals" (like trade) that we did share.

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  13. The point is science is built incrementally and one never knows where the next insight will come from that solves a major problem.

    Although I agree with this statement, it does not bear one way on the other on the question of whether "90% of published papers are insignificant".

    A good test would be to look at how many papers published, oh, 5 years ago have been cited at all (by non-overlapping authors). I have no idea what this would yield, but I would guess that a non-zero percentage of even STOC/FOCS papers are not cited. And when you look at "second-tier" venues like ICALP I am sure the percentage would be much higher (possibly approaching 90%).

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  14. I would guess that a non-zero percentage of even STOC/FOCS papers are not cited. And when you look at "second-tier" venues like ICALP I am sure the percentage would be much higher (possibly approaching 90%).

    The point is that you never know which is the 90% (**) that won't be cited.

    (**) 90% for ICALP is way too high. A small random sample suggests is more like 20%.

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  15. It depends how broadly and generally you define long term goals. Taking George as an example, he probably has the long term goal of 'making things in America good, especially for people like myself', which is of course a very good goal, certainly not evil. In this sense, I agree with Lance, and don't like when people say 'there he goes trying to destroy the American economy again' or such things -- I am certain he does not have the long term goal of destroying the American economy.

    However, when you go to just the next level of generality, like what is it he considers 'good', the goals lose their appeal to many people who shared the general goal.

    Moreover, one can have some non-evil goals that may sometimes be at odds with each other (e.g., personal power and wealth, and peace and prosperity for our nation and other nations). How one prioritizes them, may be evil.

    Finally, one may have the best of goals, but not enough skills to achieve them (even using his own strategy), and personal hangups about admitting mistakes.

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  16. I agree that it can be hard to tell what work being done now will be valuable in the long term. However, I think one can often distinguish between impressive work of questionable importance and mediocre work (and the latter is much less likely to turn out to be important later).

    Regarding anon5's comments, I largely agree, but I think the stories about Wiles are misleading. My impression is that all the papers that contributed significant insights to his approach had been previously admired as important contributions. Maybe not as important as they appeared in hindsight, but enough to get tenure at first-rate universities (such as Caltech) and definitely not something anybody would ever dismiss as "insignificant".

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  17. Elsevier, George, and the recording industry are all evil. It is silly to say "but they are not pure evil." The truth is that nobody cares about "pure" evil--we are perfectly happy to despise things which are mostly evil.

    "This paper is crap, it shouldn't be published in STOC."

    "But it's not pure crap! The bibliography _is_ arranged alphabetically after all."

    "What? You're an idiot."

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  18. This is anon5.

    one can often distinguish between impressive work of questionable importance and mediocre work (and the latter is much less likely to turn out to be important later).

    Sure, one can often distinguish as you say, but in order not to publish the remaining 90% riff-raff we need to always distinguish the mediocre work. Since we can't we publish all middle-of-the-road work.

    In terms of Wiles proof of FLT, he used many papers along the way. Some were key insights such as Frey's and Ribet's, which were certainly enough to get you tenure in a first rate university. The papers I'm refering to are not those. In fact one of the remarkable things Wiles did was read and understand a large percentage of the literature in number theory, elliptic curves, Galois theory, etc, trying to find ideas and techniques he could use in his proof.

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  19. The two parallel threads here (an 'evil' publisher vs the value of apparently marginal work) have an interesting overlap:

    The economics of for-profit publishing mean that it is in the interest of for-profit publishers to have as much content as possible to sell since their ability to charge for content is based more on the aggregate quality of their offerings than their average quality. Reduced costs for dissemination mean that they don't have much of a capacity limit. The interests of highly selective conferences are quite different because these conferences are capacity-limited.

    So, for-profit publishers are motivated to provide an outlet for work that does not make it into highly selective conferences. This will remain useful even when the capacity of selective society-published and not-for-profit journals rises to meet the need for high quality papers. (It is certainly not there yet.) Of course, when that happens it is unlikely that we will be as willing to pay as much for this service as we now do.

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  20. The real irony of it is that academics rarely see things in their own disciplines as black and white, even the most basic truths. So that many a theologian cannot decide whether or not there is a God; many a theoretical computer scientist the truth of the Church-Turing thesis; etc. Yet these same intellectuals are perfectly welling to extol their opinion as the alpha and omega about fields of which they know much less.

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  21. many a theoretical computer scientist [cannot decide] the truth of the Church-Turing thesis

    and for this absurd statement Grant shows that he has no clue about what theoretical computer scientists think.

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  22. This is anon16, responding to anon18 (= anon5).

    I agree that it would be ridiculous to restrict publication to the best papers, because we can't reliably sort out which ones will eventually be important.

    On the other hand, I'm still skeptical about the Wiles story. I don't know what the first insignificant paper was (what is a reference?). Perhaps it exists, but I haven't heard any stories about his being inspired by a paper that had previously been considered insignificant.

    As for the second paper, writing up an account of his error and why it could not be fixed would have been far from insignificant. Even before the error was corrected, his work was still a major accomplishment (correctly proving Shimura-Taniyama-Weil for infinitely many j-invariants, which would not have been enough to prove FLT but still a huge advance). Presenting the obstacles to completing his program would have been a very significant paper.

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  23. On the other hand, I'm still skeptical about the Wiles stor[...]but I haven't heard any stories about his being inspired by a paper that had previously been considered insignificant.

    Quote from Wiles:

    "...I was casually glancing at a paper of Barry Mazur's, and there was just one sentence which made a reference to actually what's a 19th century construction, and I just instantly realized that there was a trick that I could use, [...] and use that information to just go that one last step."

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  24. This is anon 1.

    I think my point was completely lost. The point was that the *goal* of most of "us" is to publish many papers (not, as some have read this to mean, to prove many important results).

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  25. To Anon # 21. I was talking not only about the Church-Turing thesis, but also the extended Church Turing thesis and, in general, the basic question of how our mathematical theorems relate to reality. I was hoping that the readers of this BLOG would naturally understand this and I wanted to trade brevity for fullness of explanation, but that seems to have been a mistake. Sorry for the confusion.

    Perhaps there are better examples to make my original point. Can you think of any better ones?

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  26. In response to Anon #17: To say that a paper is crap is already a hyperbole. The sentence should not be taken literally, but figuratively. To say a paper is crap or pure crap or mostly crap is not to literally say that it has no redeeming qualities (such as the correct ordering of the bib), but rather to say that in hyperbole.

    I am not sure what the literal difference, much less the figurative difference, between crap and pure crap is. But I think that your parody breaks down at this point. No pun intended.

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  27. Anon 1: I don't think that very many of people get into the field with the idea of having a steady stream of marginal papers that get published in major conferences. Researchers want to solve important problems, contribute significantly to the store of human knowledge, be recognized for the quality their work, have their contributions recognized for posterity. These are the prime motives, just like the prime motive of the for-profit publishers is to make money.

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  28. one sentence which made a reference to actually what's a 19th century construction:

    It's hard to say based on this quote (from the NOVA show on FLT) what this construction was (perhaps some explicit coordinates for X_0(5) or X_0(15)), but there's no reason to think it was insignificant just because it dates from the 19th century. By contrast, the fact that Mazur was mentioning it a century later suggests that he considered it significant.

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  29. Anon 27:

    Of course people "get into the field" hoping to do good science. By the time they finish their phd their goals change to publishing many papers. It's a process called socialization.

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  30. while we're making off-topic comments, there's another way to avoid linking anon4, anon16, anon28 etc and yet remaining anonymous while posting a comment.

    choose the other identity option while posting a comment, and choose a moniker that you stick with throughout.

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  31. like this

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  32. Re: the original commentary - excellent comment! It's refreshing to see an acknowledgement than an opposing side in a difficult debate doen't have to be characterized as "evil" - thanks for saying it.

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  33. Lance Fortnow and anon32 are both evil! ;)

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  34. Lance says: Scientist tend to believe the world works by simple rules and we reinforce these viewpoints by only hanging out with other scientists like ourselves. The Internet has only made things worse, as we tend to only read stuff written by people who already agree with us.

    Following up this train of thought suggests a Fermi calculation. We make the utopian assumption that one percent of the planetary GNP is devoted to fundamental research (this is a level that the UN recommends).

    On a planet with ten billion people—the projected peak for the mid-21st Century—this level of investment in fundamental research is enough to support on the order of 100 million scientists and mathematicians.

    If each publishes one article per year, then the resulting production of peer-reviewed publications will be on the order of 300,000 articles per day. That's a lot!

    We can wonder, as a practical matter, is humanity in danger of running out of new theorems and new scientific facts?

    Here is where complexity theory comes to the rescue. As Bob Hearn says in a recent Mathematical Intelligencer article entitled TipOver is NP-complete:

    "It is a curious fact that many, if not most, interesting games and puzzles seem to be NP-complete or harder. It seems as though the very features that make puzzles challenging seem to give them a kind of computational power, which is reflected in their formal complexity. What, if anything, this says about the nature of intelligence, and the appeal of puzzles, is an interesting question."

    We conclude, that neither complexity theory nor economics poses a barrier to the planetary production of 100 million scientific articles per year, with each article logically independent of all the rest!

    The reason being, that there are exponentially many real-world problems that, like the game TipOver, are in complexity class NP-hard, yet exhibit enough regularity to be solvable for important special cases.

    Elsevier and the other publication companies surely are happy about this prospect.

    Is it inevitable? I dunno, but for sure, it's going to be an interesting century. :)

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  35. The discussion about paper quality reminds me of the quote

    "Mom. why do the newspapers announce only the death of great people, but not their birth?"

    Wiles' paper is an extreme example: if we are going to have the standard that a paper is only good if it is of that standard, in a given year there is typically no paper worth publishing -- in all of Mathematics and Theoretical Computer Science.

    It is notoriously difficult to judge the worth of most papers. Let me present a bit of Complexity Theory history. In the 1978 FOCS there was a very interesting paper by Abelson,
    [journal version: Harold Abelson, Lower Bounds on Information Transfer in Distributed Computations, Journal of the ACM (JACM), v.27 n.2, p.384-392, April 1980], which was apparently influenced by earlier comments of Marvin Minsky on global vs local properties and tradeoffs in computation.

    Next year, Andy Yao presented something that, at first seemed to me like a minor technical followup: the same kind of question about lower bounds on information transmission could also be asked in the Boolean domain. The lower bound techniques would then have to be combinatorial rather than algebraic, and one could get some results. [Some complexity questions related to distributive computing", Proceedings of 11 th STOC, pp. 209-213]

    This "no big deal" was of course the paper that inspired Communication Complexity -- thanks to beautiful "minor technical improvements" that followed shortly. So, it is true that 80% of a typical STOC/FOCS conference is worthless--the problem is to figure out which 80%.
    (and of course, depends on when you make the judgement)

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  36. I'm sorry, STOC/FOCS is not the right target of this discussion. If you know about our field, then looking at a recent program, e.g. http://www.cs.washington.edu/stoc06/stoc06program.pdf just makes you extremeley proud. There are a handful of throw-away results, but also a gorgeous array of beautiful ideas, technical innovations, and groundbreaking work in many areas of TCS.

    Percentage of throw-away results (written just to get another publication, not to advance the field) by conference (in descending order):

    FOCS
    STOC
    CCC
    SOCG
    SODA
    ...

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  37. I don't think you'll get very far ranking "relevance" across subfields. To a complexity type CCC looks very relevant while SODA has lots of irrelevant algorithm papers. To a SODA type SODA is full of neat and interesting algorithm papers while CCC is all made up theoretical problems of no interest to anyone but another CCC type.

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  38. anon 29:
    Unfortunately, I tend to agree with you. I heard once someone calling this phenomenon "Fashoin TV".

    The problem with "90% of published papers are insignificant" is mainly quantitive: now it is 90% of O(50,000), while before
    it was 90% of O(5000).

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  39. Anonymous said: The problem with "90% of published papers are insignificant" is mainly quantitative: now it is 90% of O(50,000), while before it was 90% of O(5000).

    This illustrates nicely that "Quantity becomes quality". When von Neumann was doing his work on quantum measurement in the 1930s and 1940s, I checked that he needed to read only one or two papers per month.

    (By the way, it is hugely fun to read a volume of Physical Review from, e.g., 1939 ... about half the article are by famous authors, and by modern standards, they are very accessible to non-specialists.)

    Following WWII, the flow of articles increased so greatly that it became infeasible for anyone to be von Neumann (even von Neumann himself).

    Less important than the flow of articles is the flow of new ideas and new methods -- it really does seem that these are exponential in number, and therefore, are destined to increase without (essentially) any limit.

    E.g., in attempting to summarize the role of (1) quantum measurement (QM) in (2) model order reduction (QMOR) by (3) projection onto Kahler manifolds (KM), we find that the literature on these three subjects (QS:QMOR:KM) is approximately in the ratio 1:2:4.

    It turns out that there are on the order of 1000 articles on quantum measurement that could arguably be called significant, and the net literature relevant to this single QS:QMOR:KM subject is (very roughly) on the order of 10,000 articles. Yikes!

    This is not to complain, but instead merely to note, that young researchers today are experiencing challenges and opportunities that von Neumann's generation never knew.

    And further, this acceleration of the literature is only beginning -- barring some sort of planetary collapse, the flow of mathematical and scientific literature is destined to increase by tens or hundreds of times in coming decades.

    For sure, the coming century will be interesting, with unprecedented opportunities for creative thought, and also, the most urgent of incentives---planetary survival.

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  40. Re Comment 7:

    Gates' 'charity' foundation in actuality invests in for-profit activity, some of it damaging the environment. How's that for purity of evil? :-)

    http://en.wikipedia.org/wiki/Bill_and_Melinda_Gates_Foundation#Investment_in_oil_companies_and_drug_companies

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  41. Anonymous said: The problem with "90% of published papers are insignificant" is mainly quantitative: now it is 90% of O(50,000), while before it was 90% of O(5000).

    39 said:
    This illustrates nicely that "Quantity becomes quality". When von Neumann was doing his work on quantum measurement in the 1930s and 1940s, I checked that he needed to read only one or two papers per month.



    It seems that the quantity by each indivual is much higher. Do you have an explanation for this?

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